Multi-objective stable matching and distributional constraints

Abstract

In this paper, we study a centralized matching scheme that has to assign a set of agents to a set of jobs by meeting distributional constraints. The scheme has to maximize social welfare and fairness offered by the matching to the parties. Furthermore, the allocation needs to minimize the number of blocking pairs. The problem is NP-hard and hence computationally challenging. Nonetheless, the users expect good solutions that can be generated quickly. We propose linear programming-based improvement heuristics to solve this multi-criteria stable matching problem. Our approach finds an equitable and global welfare stable matching solution in significantly lesser time. We then demonstrate the applicability of our proposed model and the solution methodology in a workforce allocation problem faced by software projects.